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@article{grimm2003high,
  title={High-mass X-ray binaries as a star formation rate indicator in distant galaxies},
  author={Grimm, H-J and Gilfanov, Marat and Sunyaev, R},
  journal={Monthly Notices of the Royal Astronomical Society},
  volume={339},
  number={3},
  pages={793--809},
  year={2003},
  publisher={Blackwell Science Ltd Oxford, UK}
}
@article{kroupa2001variation,
  title={On the variation of the initial mass function},
  author={Kroupa, Pavel},
  journal={Monthly Notices of the Royal Astronomical Society},
  volume={322},
  number={2},
  pages={231--246},
  year={2001},
  publisher={Blackwell Science Ltd Oxford, UK}
}
@article{kroupa1993distribution,
  title={The distribution of low-mass stars in the Galactic disc},
  author={Kroupa, Pavel and Tout, Christopher A and Gilmore, Gerard},
  journal={Monthly Notices of the Royal Astronomical Society},
  volume={262},
  number={3},
  pages={545--587},
  year={1993},
  publisher={Oxford University Press Oxford, UK}
}

@article{hurley2002evolution,
  title={Evolution of binary stars and the effect of tides on binary populations},
  author={Hurley, Jarrod R and Tout, Christopher A and Pols, Onno R},
  journal={Monthly Notices of the Royal Astronomical Society},
  volume={329},
  number={4},
  pages={897--928},
  year={2002},
  publisher={The Royal Astronomical Society}
}
@article{wiktorowicz2019observed,
  title={The Observed versus Total Population of ULXs},
  author={Wiktorowicz, Grzegorz and Lasota, Jean-Pierre and Middleton, Matthew and Belczynski, Krzysztof},
  journal={The Astrophysical Journal},
  volume={875},
  number={1},
  pages={53},
  year={2019},
  publisher={IOP Publishing}
}
@article{hobbs2005statistical,
  title={A statistical study of 233 pulsar proper motions},
  author={Hobbs, George and Lorimer, DR and Lyne, AG and Kramer, M},
  journal={Monthly Notices of the Royal Astronomical Society},
  volume={360},
  number={3},
  pages={974--992},
  year={2005},
  publisher={Blackwell Science Ltd Oxford, UK}
}

@article{shakura1973black,
  title={Black holes in binary systems. Observational appearance.},
  author={Shakura, Ni I and Sunyaev, Rashid Alievich},
  journal={Astronomy and Astrophysics},
  volume={24},
  pages={337--355},
  year={1973}
}

@article{poutanen2007supercritically,
  title={Supercritically accreting stellar mass black holes as ultraluminous X-ray sources},
  author={Poutanen, Juri and Lipunova, Galina and Fabrika, Sergei and Butkevich, Alexey G and Abolmasov, Pavel},
  journal={Monthly Notices of the Royal Astronomical Society},
  volume={377},
  number={3},
  pages={1187--1194},
  year={2007},
  publisher={Blackwell Publishing Ltd Oxford, UK}
}



@article{king2009masses,
  title={Masses, beaming and Eddington ratios in ultraluminous X-ray sources},
  author={King, AR},
  journal={Monthly Notices of the Royal Astronomical Society: Letters},
  volume={393},
  number={1},
  pages={L41--L44},
  year={2009},
  publisher={Blackwell Science Ltd Oxford, UK}
}


@article{king2014hlx,
  title={HLX-1 may be an SS433 system},
  author={King, Andrew and Lasota, Jean-Pierre},
  journal={Monthly Notices of the Royal Astronomical Society: Letters},
  volume={444},
  number={1},
  pages={L30--L33},
  year={2014},
  publisher={Oxford University Press}
}
@article{king2016ulxs,
  title={ULXs: Neutron stars versus black holes},
  author={King, Andrew and Lasota, Jean--Pierre},
  journal={Monthly Notices of the Royal Astronomical Society: Letters},
  volume={458},
  number={1},
  pages={L10--L13},
  year={2016},
  publisher={The Royal Astronomical Society}
}
@article{king2017pulsing,
  title={Pulsing ULXs: tip of the iceberg?},
  author={King, Andrew and Lasota, Jean-Pierre and Klu{\'z}niak, W{\l}odek},
  journal={Monthly Notices of the Royal Astronomical Society: Letters},
  volume={468},
  number={1},
  pages={L59--L62},
  year={2017},
  publisher={Oxford University Press}
}
@article{king2008accretion,
  title={Accretion rates and beaming in ultraluminous X-ray sources},
  author={King, AR},
  journal={Monthly Notices of the Royal Astronomical Society: Letters},
  volume={385},
  number={1},
  pages={L113--L115},
  year={2008},
  publisher={The Royal Astronomical Society}
}

@article{wiktorowicz2017origin,
  title={The origin of the Ultraluminous X-ray Sources},
  author={Wiktorowicz, Grzegorz and Sobolewska, Ma{\l}gorzata and Lasota, Jean-Pierre and Belczynski, Krzysztof},
  journal={The Astrophysical Journal},
  volume={846},
  number={1},
  pages={17},
  year={2017},
  publisher={IOP Publishing}
}

@article{el2019wind,
  title={Wind Roche lobe overflow in high-mass X-ray binaries-A possible mass-transfer mechanism for ultraluminous X-ray sources},
  author={El Mellah, I and Sundqvist, JO and Keppens, R},
  journal={Astronomy \& Astrophysics},
  volume={622},
  pages={L3},
  year={2019},
  publisher={EDP Sciences}
}

@article{bondi1944mechanism,
  title={On the mechanism of accretion by stars},
  author={Bondi, Hermann and Hoyle, Fred},
  journal={Monthly Notices of the Royal Astronomical Society},
  volume={104},
  number={5},
  pages={273--282},
  year={1944},
  publisher={Narnia}
}
@article{edgar2004review,
  title={A review of Bondi--Hoyle--Lyttleton accretion},
  author={Edgar, Richard},
  journal={New Astronomy Reviews},
  volume={48},
  number={10},
  pages={843--859},
  year={2004},
  publisher={Elsevier}
}

@article{eggleton1983aproximations,
  title={Aproximations to the radii of Roche lobes.},
  author={Eggleton, Peter P},
  journal={apj},
  volume={268},
  pages={368--369},
  year={1983}
}

@article{liu2013puzzling,
  title={Puzzling accretion onto a black hole in the ultraluminous X-ray source M 101 ULX-1},
  author={Liu, Ji-Feng and Bregman, Joel N and Bai, Yu and Justham, Stephen and Crowther, Paul},
  journal={Nature},
  volume={503},
  number={7477},
  pages={500--503},
  year={2013},
  publisher={Nature Publishing Group}
}

@article{furst2018tale,
  title={A tale of two periods: determination of the orbital ephemeris of the super-Eddington pulsar NGC 7793 P13},
  author={F{\"u}rst, Felix and Walton, DJ and Heida, M and Harrison, FA and Barret, D and Brightman, M and Fabian, AC and Middleton, MJ and Pinto, C and Rana, V and others},
  journal={Astronomy \& Astrophysics},
  volume={616},
  pages={A186},
  year={2018},
  publisher={EDP Sciences}
}
@article{wolter2018x,
  title={The X-Ray Luminosity Function of Ultraluminous X-Ray Sources in Collisional Ring Galaxies},
  author={Wolter, Anna and Fruscione, Antonella and Mapelli, Michela},
  journal={The Astrophysical Journal},
  volume={863},
  number={1},
  pages={43},
  year={2018},
  publisher={IOP Publishing}
}

@article{yungelson1997rate,
  title={On the rate of novae in galaxies of different types},
  author={Yungelson, L and Livio, M and Tutukov, A},
  journal={The Astrophysical Journal},
  volume={481},
  number={1},
  pages={127},
  year={1997},
  publisher={IOP Publishing}
}

@report{,
   abstract = {We present a comprehensive description of the population synthesis code StarTrack. The original code has been significantly modified and updated. Special emphasis is placed here on processes leading to the formation and further evolution of compact objects (white dwarfs, neutron stars, and black holes). Both single and binary star populations are considered. The code now incorporates detailed calculations of all mass transfer phases, a full implementation of orbital evolution due to tides, as well as the most recent estimates of magnetic braking. This updated version of StarTrack can be used for a wide variety of problems, with relevance to observations with many current and planned observatories, e.g., studies of X-ray binaries (Chandra, XMM-Newton), gravitational radiation sources (LIGO, LISA), and gamma-ray burst progenitors (HETE-II, Swift). The code has already been used in studies of Galactic and extra-galactic X-ray binary populations, black holes in young star clusters, Type Ia supernova progenitors, and double compact object populations. Here we describe in detail the input physics, we present the code calibration and tests, and we outline our current studies in the context of X-ray binary populations.},
   author = {Krzysztof Belczynski and Vassiliki Kalogera and Frederic A Rasio and Ronald E Taam and Andreas Zezas and Tomasz Bulik and Thomas J Maccarone and Natalia Ivanova},
   keywords = {Subject headings,binaries,close-black hole physics-stars,evolution-stars,neutron-white dwarfs-X-rays},
   title = {COMPACT OBJECT MODELING WITH THE STARTRACK POPULATION SYNTHESIS CODE},
}
@article{Shao2014,
   abstract = {Be stars are rapidly rotating B-type stars. The origin of their rapid rotation is not certain, but binary interaction remains as a possibility. In this work, we investigate the formation of Be stars resulting from mass transfer in binaries in the Galaxy. We calculate binary evolution with both stars evolving simultaneously and consider different possible mass accretion histories for the accretor. From the calculated results, we obtain the critical mass ratios qcr that determine the stability of the mass transfer. We also numerically calculate the parameter λ in common envelope evolution and then incorporate both qcr and λ into the population synthesis calculations. We present the predicted numbers and characteristics of Be stars in binary systems with different types of companions, including helium stars, white dwarfs, neutron stars, and black holes. We find that in Be/neutron star binaries, the Be stars can have a lower mass limit ∼8 M⊙ if they are formed by stable (i.e., without the occurrence of common envelope evolution) and nonconservative mass transfer. We demonstrate that isolated Be stars may originate from both mergers of two main-sequence stars and disrupted Be binaries during the supernova explosions of the primary stars, but mergers seem to play a much more important role. Finally, the fraction of Be stars that have involved binary interactions in all B-type stars can be as high as ∼13%-30%, implying that most Be stars may result from binary interaction.},
   author = {Yong Shao and Xiang Dong Li},
   doi = {10.1088/0004-637X/796/1/37},
   issn = {15384357},
   issue = {1},
   journal = {Astrophysical Journal},
   keywords = {X-rays: binaries,X-rays: stars,binaries: close,stars: emission-line, Be,stars: evolution},
   month = {11},
   publisher = {Institute of Physics Publishing},
   title = {On the formation of Be stars through binary interaction},
   volume = {796},
   year = {2014},
}
@article{Swartz2011,
   abstract = {One hundred seven ultraluminous X-ray sources (ULXs) with 0.3-10.0keV luminosities in excess of 1039ergs-1 are identified in a complete sample of 127 nearby galaxies. The sample includes all galaxies within 14.5Mpc above the completeness limits of both the Uppsala Galaxy Catalogue and the Infrared Astronomical Satellite survey. The galaxy sample spans all Hubble types, a four-decade range in mass, 7.5 < log (M/M·) < 11.4, and in star formation rate, 0.0002 < SFR(M· yr -1) ≤ 3.6. ULXs are detected in this sample at rates of one per 3.2 × 1010 M·, one per 0.5 M ·yr-1 star formation rate, and one per 57Mpc 3 corresponding to a luminosity density of 2 × 10 37ergs-1Mpc-3. At these rates we estimate as many as 19 additional ULXs remain undetected in fainter dwarf galaxies within the survey volume. An estimated 14 objects, or 13%, of the 107 ULX candidates are expected to be background sources. The differential ULX luminosity function shows a power-law slope α -0.8 to -2.0 with an exponential cutoff at 20 × 1039ergs-1 with precise values depending on the model and on whether the ULX luminosities are estimated from their observed numbers of counts or, for a subset of candidates, from their spectral shapes. Extrapolating the observed luminosity function predicts at most one very luminous ULX, LX 1041ergs-1, within a distance as small as 100Mpc. The luminosity distribution of ULXs within the local universe cannot account for the recent claims of luminosities in excess of 2 × 1041ergs-1, requiring a new population class to explain these extreme objects. © 2011 The American Astronomical Society. All rights reserved.},
   author = {Douglas A. Swartz and Roberto Soria and Allyn F. Tennant and Mihoko Yukita},
   doi = {10.1088/0004-637X/741/1/49},
   issn = {15384357},
   issue = {1},
   journal = {Astrophysical Journal},
   keywords = {X-rays: binaries,X-rays: galaxies,X-rays: general,galaxies: general,surveys},
   month = {11},
   note = {XLF fits in 2011.},
   publisher = {Institute of Physics Publishing},
   title = {A complete sample of ultraluminous x-ray source host galaxies},
   volume = {741},
   year = {2011},
}
@generic{Wiktorowicz2017,
   abstract = {Recently, several ultraluminous X-ray (ULX) sources were shown to host a neutron star (NS) accretor. We perform a suite of evolutionary calculations which show that, in fact, NSs are the dominant type of ULX accretor. Although black holes (BH) dominate early epochs after the star-formation burst, NSs outweigh them after a few 100 Myr and may appear as late as a few Gyr after the end of the star formation episode. If star formation is a prolonged and continuous event (i.e., not a relatively short burst), NS accretors dominate ULX population at any time in solar metallicity environment, whereas BH accretors dominate when the metallicity is sub-solar. Our results show a very clear (and testable) relation between the companion/donor evolutionary stage and the age of the system. A typical NS ULX consists of a ~ 1.3M⊙NS and ~ 1.0M⊙Red Giant. A typical BH ULX consist of a ~ 8M⊙BH and ~ 6M⊙main-sequence star. Additionally, we find that the very luminous ULXs (LX & 1041erg/s) are predominantly BH systems (~ 9M⊙) with Hertzsprung gap donors (~ 2M⊙). Nevertheless, some NS ULX systems may also reach extremely high X-ray luminosities (1041erg/s). Subject headings. stars. black holes, neutron stars, X-ray binaries.},
   author = {Grzegorz Wiktorowicz and Małgorzata Sobolewska and Jean Pierre Lasota and Krzysztof Belczynski},
   doi = {10.3847/1538-4357/aa821d},
   issn = {0004-637X},
   journal = {arXiv},
   keywords = {Neutron stars,Stars: black holes,X-ray binaries},
   month = {5},
   publisher = {arXiv},
   title = {The origin of the ultraluminous X-ray sources},
   year = {2017},
}
@article{Shao2015,
   abstract = {Most ultraluminous X-ray sources (ULXs) are believed to be X-ray binary systems, but previous observational and theoretical studies tend to prefer a black hole rather than a neutron star (NS) accretor. The recent discovery of 1.37 s pulsations from the ULX M82 X-2 has established its nature as a magnetized NS. In this work we model the formation history of NS ULXs in an M82- or Milky Way (MW)-like Galaxy, by use of both binary population synthesis and detailed binary evolution calculations. We find that the birth rate is around 10-4 yr-1 for the incipient X-ray binaries in both cases. We demonstrate the distribution of the ULX population in the donor mass-orbital period plane. Our results suggest that, compared with black hole X-ray binaries, NS X-ray binaries may significantly contribute to the ULX population, and high-mass and intermediate-mass X-ray binaries dominate the NS ULX population in M82- and MW-like Galaxies, respectively.},
   author = {Yong Shao and Xiang Dong Li},
   doi = {10.1088/0004-637X/802/2/131},
   issn = {15384357},
   issue = {2},
   journal = {Astrophysical Journal},
   keywords = {Accretion, accretion disks,Stars: evolution,Stars: neutron,X-rays: binaries},
   month = {4},
   publisher = {Institute of Physics Publishing},
   title = {A population of ultraluminous X-ray sources with an accreting neutron star},
   volume = {802},
   year = {2015},
}
@generic{Wiktorowicz2017,
   abstract = {Recently, several ultraluminous X-ray (ULX) sources were shown to host a neutron star (NS) accretor. We perform a suite of evolutionary calculations which show that, in fact, NSs are the dominant type of ULX accretor. Although black holes (BH) dominate early epochs after the star-formation burst, NSs outweigh them after a few 100 Myr and may appear as late as a few Gyr after the end of the star formation episode. If star formation is a prolonged and continuous event (i.e., not a relatively short burst), NS accretors dominate ULX population at any time in solar metallicity environment, whereas BH accretors dominate when the metallicity is sub-solar. Our results show a very clear (and testable) relation between the companion/donor evolutionary stage and the age of the system. A typical NS ULX consists of a ~ 1.3M⊙NS and ~ 1.0M⊙Red Giant. A typical BH ULX consist of a ~ 8M⊙BH and ~ 6M⊙main-sequence star. Additionally, we find that the very luminous ULXs (LX & 1041erg/s) are predominantly BH systems (~ 9M⊙) with Hertzsprung gap donors (~ 2M⊙). Nevertheless, some NS ULX systems may also reach extremely high X-ray luminosities (1041erg/s). Subject headings. stars. black holes, neutron stars, X-ray binaries.},
   author = {Grzegorz Wiktorowicz and Małgorzata Sobolewska and Jean Pierre Lasota and Krzysztof Belczynski},
   doi = {10.3847/1538-4357/aa821d},
   issn = {0004-637X},
   journal = {arXiv},
   keywords = {Neutron stars,Stars: black holes,X-ray binaries},
   month = {5},
   publisher = {arXiv},
   title = {The origin of the ultraluminous X-ray sources},
   year = {2017},
}
@article{Wolter2018,
   author = {Anna Wolter and Antonella Fruscione and Michela Mapelli},
   doi = {10.3847/1538-4357/aacb34},
   issn = {1538-4357},
   issue = {1},
   journal = {The Astrophysical Journal},
   month = {8},
   note = {Obsevation of ULX, which I mainly compared with},
   pages = {43},
   title = {The X-Ray Luminosity Function of Ultraluminous X-Ray Sources in Collisional Ring Galaxies},
   volume = {863},
   url = {https://iopscience.iop.org/article/10.3847/1538-4357/aacb34},
   year = {2018},
}
@generic{Kaaret2017,
   abstract = {We review observations of ultraluminous X-ray sources (ULXs). X-ray spectroscopic and timing studies of ULXs suggest a new accretion state distinct from those seen in Galactic stellar-mass black hole binaries. The detection of coherent pulsations indicates the presence of neutron-star accretors in three ULXs and therefore apparently super-Eddington luminosities. Optical and X-ray line profiles of ULXs and the properties of associated radio and optical nebulae suggest that ULXs produce powerful outflows, also indicative of super-Eddington accretion. We discuss models of super-Eddington accretion and their relationship to the observed behaviors of ULXs. We review the evidence for intermediate-mass black holes (IMBHs) in ULXs. We consider the implications of ULXs for super-Eddington accretion in active galactic nuclei, heating of the early Universe, and the origin of the black hole binary recently detected via gravitational waves.},
   author = {Philip Kaaret and Hua Feng and Timothy P. Roberts},
   doi = {10.1146/annurev-astro-091916-055259},
   issn = {00664146},
   journal = {Annual Review of Astronomy and Astrophysics},
   keywords = {Accretion physics,Black holes,Neutron stars,X-ray binaries,X-rays: galaxies},
   month = {8},
   note = {Review of ULX},
   pages = {303-341},
   publisher = {Annual Reviews Inc.},
   title = {Ultraluminous X-Ray Sources},
   volume = {55},
   year = {2017},
}
@report{Hurley2000,
   abstract = {We present a rapid binary evolution algorithm that enables modelling of even the most complex binary systems. In addition to all aspects of single star evolution, features such as mass transfer, mass accretion, common-envelope evolution, collisions, supernova kicks and angular momentum loss mechanisms are included. In particular, circularization and synchronization of the orbit by tidal interactions are calculated for convective, radiative and degenerate damping mechanisms. We use this algorithm to study the formation and evolution of various binary systems. We also investigate the effect that tidal friction has on the outcome of binary evolution. Using the rapid binary code, we generate a series of large binary populations and evaluate the formation rate of interesting individual species and events. By comparing the results for populations with and without tidal friction we quantify the hitherto ignored systematic effect of tides and show that modelling of tidal evolution in binary systems is necessary in order to draw accurate conclusions from population synthesis work. Tidal synchronism is important but because orbits generally circularize before Roche-lobe overflow the outcome of the interactions of systems with the same semi-latus rectum is almost independent of eccentricity. It is not necessary to include a distribution of eccentricities in population synthesis of interacting binaries, however, the initial separations should be distributed according to the observed distribution of semi-latera recta rather than periods or semi-major axes.},
   author = {Jarrod R Hurley and Christopher A Tout and Onno R Pols},
   journal = {Mon. Not. R. Astron. Soc},
   keywords = {analytic-methods,cataclysmic variables-galaxies,evolution-binaries,general-stars,methods,statistical-stars,stellar content},
   pages = {1-36},
   title = {Evolution of Binary Stars and the Effect of Tides on Binary Populations},
   volume = {000},
   year = {2000},
}
@report{Hurley2000,
   abstract = {We present a rapid binary evolution algorithm that enables modelling of even the most complex binary systems. In addition to all aspects of single star evolution, features such as mass transfer, mass accretion, common-envelope evolution, collisions, supernova kicks and angular momentum loss mechanisms are included. In particular, circularization and synchronization of the orbit by tidal interactions are calculated for convective, radiative and degenerate damping mechanisms. We use this algorithm to study the formation and evolution of various binary systems. We also investigate the effect that tidal friction has on the outcome of binary evolution. Using the rapid binary code, we generate a series of large binary populations and evaluate the formation rate of interesting individual species and events. By comparing the results for populations with and without tidal friction we quantify the hitherto ignored systematic effect of tides and show that modelling of tidal evolution in binary systems is necessary in order to draw accurate conclusions from population synthesis work. Tidal synchronism is important but because orbits generally circularize before Roche-lobe overflow the outcome of the interactions of systems with the same semi-latus rectum is almost independent of eccentricity. It is not necessary to include a distribution of eccentricities in population synthesis of interacting binaries, however, the initial separations should be distributed according to the observed distribution of semi-latera recta rather than periods or semi-major axes.},
   author = {Jarrod R Hurley and Christopher A Tout and Onno R Pols},
   journal = {Mon. Not. R. Astron. Soc},
   keywords = {analytic-methods,cataclysmic variables-galaxies,evolution-binaries,general-stars,methods,statistical-stars,stellar content},
   pages = {1-36},
   title = {Evolution of Binary Stars and the Effect of Tides on Binary Populations},
   volume = {000},
   year = {2000},
}
@article{Wiktorowicz2019,
   abstract = {We have analyzed how anisotropic emission of radiation affects the observed sample of ultraluminous X-ray sources (ULXs) by performing simulations of the evolution of stellar populations, employing recent developments in stellar and binary physics, and by utilizing a geometrical beaming model motivated by theory and observation. Whilst ULXs harboring black hole accretors (BH ULXs) are typically emitting isotropically, the majority of ULXs with neutron star accretors (NS ULXs) are found to be beamed. These findings confirm previous assertions that a significant fraction of ULXs are hidden from view due to a substantial misalignment of the emission beam and the line-of-sight. We find the total number of NS ULXs in regions with constant star formation, solar metallicity, and ages above ~1 Gyr to be higher than the BH ULXs, although observationally both populations are comparable. For lower metallicities BH ULX dominate both the total and observed ULX populations. As far as burst star-formation is concerned, young ULX populations are dominated by BH ULXs, but this changes as the population ages and, post star-formation, NS ULXs dominate both the observed and total population of ULXs. We also compare our simulation output to a previous analytical prediction for the relative ratio of BH to NS ULXs in idealized flux-limited observations and find broad agreement for all but the lowest metallicities. In so doing we find that in such surveys the observed ULX population should be heavily dominated by black-hole systems rather than by systems containing neutron stars.},
   author = {Grzegorz Wiktorowicz and Jean-Pierre Lasota and Matthew Middleton and Krzysztof Belczynski},
   doi = {10.3847/1538-4357/ab0f27},
   issn = {1538-4357},
   issue = {1},
   journal = {The Astrophysical Journal},
   month = {4},
   pages = {53},
   publisher = {American Astronomical Society},
   title = {The Observed versus Total Population of ULXs},
   volume = {875},
   year = {2019},
}
@generic{King2008,
   abstract = {I show that extreme beaming factors b are not needed to explain ultraluminous X-ray sources (ULXs) as stellar-mass binaries. For neutron-star accretors, one typically requires b ~ 0.13, and for black holes almost no beaming (b ~ 0.8). The main reason for the high apparent luminosity is the logarithmic increase in the limiting luminosity for super-Eddington accretion. The required accretion rates are explicable in terms of thermal-time-scale mass transfer from donor stars of mass 6-10 M⊙, or possibly transient outbursts. Beaming factors ≲0.1 would be needed to explain luminosities significantly above 1040L40 ergs-1, but these requirements are relaxed somewhat if the accreting matter has low hydrogen content. © 2008 The Author. Journal compilation © 2008 RAS.},
   author = {A. R. King},
   doi = {10.1111/j.1745-3933.2008.00444.x},
   issn = {17453933},
   issue = {1},
   journal = {Monthly Notices of the Royal Astronomical Society: Letters},
   keywords = {Accretion, accretion discs,Binaries: close,Black hole physics,X-rays: binaries},
   month = {3},
   note = {beaming for the first time, including the analysis of relation between beaming and Mdot},
   title = {Accretion rates and beaming in ultraluminous X-ray sources},
   volume = {385},
   year = {2008},
}
@article{,
   abstract = {Ultraluminous X-ray sources (ULXs) have such high X-ray luminosities that they were long thought to be accreting intermediate-mass black holes. Yet, some ULXs have been shown to display periodic modulations and coherent pulsations suggestive of a neutron star in orbit around a stellar companion and accreting at super-Eddington rates. In this Letter, we propose that the mass transfer in ULXs could be qualitatively the same as in supergiant X-ray binaries (SgXBs), with a wind from the donor star highly beamed towards the compact object. Since the star does not fill its Roche lobe, this mass transfer mechanism known as "wind Roche lobe overflow" can remain stable even for large donor-star-to-accretor mass ratios. Based on realistic acceleration profiles derived from spectral observations and modeling of the stellar wind, we compute the bulk motion of the wind to evaluate the fraction of the stellar mass outflow entering the region of gravitational predominance of the compact object. The density enhancement towards the accretor leads to mass-transfer rates systematically much larger than the mass-accretion rates derived by the Bondi-Hoyle-Lyttleton formula. We identify orbital and stellar conditions for a SgXBs to transfer mass at rates necessary to reach the ULX luminosity level. These results indicate that Roche-lobe overflow is not the only way to funnel large quantities of material into the Roche lobe of the accretor. With the stellar mass-loss rates and parameters of M101 ULX-1 and NGC 7793 P13, wind Roche-lobe overflow can reproduce mass-transfer rates that qualify an object as an ULX.},
   author = {I. El Mellah and J. O. Sundqvist and R. Keppens},
   doi = {10.1051/0004-6361/201834543},
   issn = {14320746},
   journal = {Astronomy and Astrophysics},
   keywords = {Accretion,Accretion disks,Outflows,Stars: black holes,Stars: neutron,Stars: winds,Supergiants,X-rays: binaries},
   month = {1},
   note = {wind RL, which I am paying attention to.},
   publisher = {EDP Sciences},
   title = {Wind Roche lobe overflow in high-mass X-ray binaries: A possible mass-transfer mechanism for ultraluminous X-ray sources},
   volume = {622},
   year = {2019},
}
@generic{King2009,
   abstract = {I suggest that the beaming factor in bright ultraluminous X-ray sources (ULXs) varies as b ∝ ṁ-2, where m is the Eddington ratio for accretion. This is required by the observed universal Lsoft ∝ T-4 relation between soft-excess luminosity and temperature, and is reasonable on general physical grounds. The beam scaling means that all observable properties of bright ULXs depend essentially only on the Eddington ratio m, and that these systems vary mainly because the beaming is sensitive to the Eddington ratio. This suggests that bright ULXs are stellar-mass systems accreting at Eddington ratios of the order of 10-30, with beaming factors b ≳ 0.1. Lower luminosity ULXs follow bolometric (not soft-excess) L ~ T4 correlations and probably represent sub-Eddington accretion on to black holes with masses ~10M⊙. High-mass X-ray binaries containing black holes or neutron stars and undergoing rapid thermal-or nuclear-time-scale mass transfer are excellent candidates for explaining both types. If the b ∝ ṁ-2 scaling for bright ULXs can be extrapolated to the Eddington ratios found in SS433, some objects currently identified as active galactic nuclei at modest redshifts might actually be ULXs ('pseudo-blazars'). This may explain cases where the active source does not coincide with the centre of the host galaxy. © 2008 The Author. Journal compilation © 2008 RAS.},
   author = {A. R. King},
   doi = {10.1111/j.1745-3933.2008.00594.x},
   issn = {17453933},
   issue = {1},
   journal = {Monthly Notices of the Royal Astronomical Society: Letters},
   keywords = {Accretion, accretion discs,BL lacertae objects: general,Binaries: close,Black hole physics,Galaxies: active,X-rays: binaries},
   month = {2},
   title = {Masses, beaming and eddington ratios in ultraluminous X-ray sources},
   volume = {393},
   year = {2009},
}
@article{Kroupa2001,
   abstract = {A universal initial mass function (IMF) is not intuitive, but so far no convincing evidence for a variable IMF exists. The detection of systematic variations of the IMF with star-forming conditions would be the Rosetta Stone for star formation. In this contribution an average or Galactic-field IMF is defined, stressing that there is evidence for a change in the power-law index at only two masses: near 0.5 M⊙ and near 0.08 M⊙. Using this supposed universal IMF, the uncertainty inherent in any observational estimate of the IMF is investigated by studying the scatter introduced by Poisson noise and the dynamical evolution of star clusters. It is found that this apparent scatter reproduces quite well the observed scatter in power-law index determinations, thus defining the fundamental limit within which any true variation becomes undetectable. The absence of evidence for a variable IMF means that any true variation of the IMF in well-studied populations must be smaller than this scatter. Determinations of the power-law indices α are subject to systematic errors arising mostly from unresolved binaries. The systematic bias is quantified here, with the result that the single-star IMFs for young star clusters are systematically steeper by Δα ≈ 0.5 between 0.1 and 1 M⊙ than the Galactic-field IMF, which is populated by, on average, about 5-Gyr-old stars. The MFs in globular clusters appear to be, on average, systematically flatter than the Galactic-field IMF (Piotto & Zoccali; Paresce & De Marchi), and the recent detection of ancient white-dwarf candidates in the Galactic halo and the absence of associated low-mass stars (Ibata et al.; Méndez & Minniti) suggest a radically different IMF for this ancient population. Star formation in higher metallicity environments thus appears to produce relatively more low-mass stars. While still tentative, this is an interesting trend, being consistent with a systematic variation of the IMF as expected from theoretical arguments.},
   author = {Pavel Kroupa},
   doi = {10.1046/j.1365-8711.2001.04022.x},
   issn = {00358711},
   issue = {2},
   journal = {Monthly Notices of the Royal Astronomical Society},
   keywords = {Binaries: general,Globular clusters: general,Open clusters and associations: general,Stars: formation,Stars: kinematics,Stars: luminosity function, mass function},
   month = {4},
   pages = {231-246},
   title = {On the variation of the initial mass function},
   volume = {322},
   year = {2001},
}
@article{Kovlakas2020,
   abstract = {Using the Chandra Source Catalog 2.0 and a newly compiled catalogue of galaxies in the local Universe, we deliver a census of ultraluminous X-ray source (ULX) populations in nearby galaxies. We find 629 ULX candidates in 309 galaxies with distance smaller than 40\,Mpc. The foreground/background contamination is $\{\sim\}20\%$. The ULX populations in bona-fide star-forming galaxies scale on average with star-formation rate (SFR) and stellar mass ($M_\star$) such that the number of ULXs per galaxy is $0.45^\{+0.06\}_\{-0.09\}\times\frac\{\rm SFR\}\{\rm M_\odot\,yr^\{-1\}\}\{+\}3.3^\{+3.8\}_\{-3.2\}\times\frac\{M_\star\}\{\rm M_\odot\}$. The scaling depends strongly on the morphological type. This analysis shows that early spiral galaxies contain an additional population of ULXs that scales with $M_\star$. We also confirm the strong anti-correlation of the ULX rate with the host galaxy's metallicity. In the case of early-type galaxies we find that there is a non-linear dependence of the number of ULXs with $M_\star$, which is interpreted as the result of star-formation history differences. Taking into account age and metallicity effects, we find that the predictions from X-ray binary population synthesis models are consistent with the observed ULX rates in early-type galaxies, as well as, spiral/irregular galaxies.},
   author = {Konstantinos Kovlakas and Andreas Zezas and Jeff J. Andrews and Antara Basu-Zych and Tassos Fragos and Ann Hornschemeier and Bret Lehmer and Andrew Ptak},
   doi = {10.1093/mnras/staa2481},
   month = {8},
   title = {A census of ultraluminous X-ray sources in the local Universe},
   url = {http://arxiv.org/abs/2008.10572 http://dx.doi.org/10.1093/mnras/staa2481},
   year = {2020},
}
@article{Grimm2003,
   abstract = {Based on Chandra and ASCA observations of nearby starburst galaxies and RXTE/ASM, ASCA and MIR-KVANT/TTM studies of high-mass X-ray binary (HMXB) populations in the Milky Way and Magellanic Clouds, we propose that the number and/or the collective X-ray luminosity of HMXBs can be used to measure the star formation rate (SFR) of a galaxy. We show that, within the accuracy of the presently available data, a linear relation between HMXB number and star formation rate exists. The relation between SFR and collective luminosity of HMXBs is non-linear in the low-SFR regime, LX ∝ SFR ∼1.7 and becomes linear only for a sufficiently high star formation rate, SFR ≳ 4.5 M⊙ yr∼1 (for M* > 8M⊙). The non-linear LX-SFR dependence in the low-SFR limit is not related to non-linear SFR-dependent effects in the population of HMXB sources. It is rather caused by the fact that we measure the collective luminosity of a population of discrete sources, which might be dominated by the few brightest sources. Although more subtle SFR-dependent effects are likely to exist, over the entire range of SFRs the data are broadly consistent with the existence of a universal luminosity function of HMXBs that can be roughly described as a power law with a differential slope of ∼1.6, a cut-off at Lx∼ few x 10 40 erg s-1 and a normalization proportional to the star formation rate. We apply our results to (spatially unresolved) starburst galaxies observed by Chandra at redshifts up to z ∼ 1.2 in the Hubble Deep Field North and show that the calibration of the collective luminosity of HMXBs as an SFR indicator based on the local sample agrees well with the SFR estimates obtained for these distant galaxies with conventional methods.},
   author = {H. J. Grimm and M. Gilfanov and R. Sunyaev},
   doi = {10.1046/j.1365-8711.2003.06224.x},
   issn = {00358711},
   issue = {3},
   journal = {Monthly Notices of the Royal Astronomical Society},
   keywords = {Galaxies: Starburst,X-rays: Binaries,X-rays: Galaxies},
   month = {3},
   pages = {793-809},
   title = {High-mass X-ray binaries as a star formation rate indicator in distant galaxies},
   volume = {339},
   year = {2003},
}
@article{Kuruwita2020,
   abstract = {Aims: Our goal is to investigate how the strength of episodic accretion bursts depends on eccentricity. Methods: We investigate the binary trigger hypothesis in longer-period (>20yr) binaries by carrying out three-dimensional magnetohydrodynamical (MHD) simulations of the formation of low-mass binary stars down to final separations of $\sim$10$\au$, including the effects of gas turbulence and magnetic fields. We ran two simulations with an initial turbulent gas core of one solar mass each and two different initial turbulent Mach numbers, M = 0.1 and M=0.2, for 6500yr after protostar formation. Results: We observe bursts of accretion at periastron during the early stages when the eccentricity of the binary system is still high. We find that this correlation between bursts of accretion and passing periastron breaks down at later stages because of the gradual circularisation of the orbits. For eccentricities greater than e=0.2, we observe episodic accretion triggered near periastron. However, we do not find any strong correlation between the strength of episodic accretion and eccentricity. The strength of accretion is defined as the ratio of the burst accretion rate to the quiescent accretion rate.We determine that accretion events are likely triggered by torques between the rotation of the circumstellar disc and the approaching binary stars. We compare our results with observational data of episodic accretion in short-period binaries and find good agreement between our simulations and the observations. Conclusions: We conclude that episodic accretion is a universal mechanism operating in eccentric young binary-star systems, independent of separation, and it should be observable in long-period binaries as well as in short-period binaries. Nevertheless, the strength depends on the torques and hence the separation at periastron.},
   author = {R. Kuruwita and C. Federrath and T. Haugbølle},
   doi = {10.1051/0004-6361/202038181},
   month = {4},
   title = {The dependence of episodic accretion on eccentricity during the formation of binary stars},
   url = {http://arxiv.org/abs/2004.07523 http://dx.doi.org/10.1051/0004-6361/202038181},
   year = {2020},
}
@article{Lehmer2020,
   abstract = {We present detailed constraints on the metallicity dependence of the high mass X-ray binary (HMXB) X-ray luminosity function (XLF). We analyze ~5 Ms of Chandra data for 55 actively star-forming galaxies at D < 30 Mpc with gas-phase metallicities spanning 12 + log(O/H) = 7-9.2. Within the galactic footprints, our sample contains a total of 1311 X-ray point sources, of which ~49% are expected to be HMXBs, with the remaining sources likely to be low-mass X-ray binaries (LMXBs; ~22%) and unrelated background sources (~29%). We construct a model that successfully characterizes the average HMXB XLF over the full metallicity range. We demonstrate that the SFR-normalized HMXB XLF shows clear trends with metallicity, with steadily increasing numbers of luminous and ultraluminous X-ray sources (logL(erg/s) = 38-40.5) with declining metallicity. However, we find that the low-luminosity (logL(erg/s) = 36-38) HMXB XLF appears to show a nearly constant SFR scaling and slope with metallicity. Our model provides a revised scaling relation of integrated LX/SFR versus 12 + log(O/H) and a new characterization of its the SFR-dependent stochastic scatter. The general trend of this relation is broadly consistent with past studies based on integrated galaxy emission; however, our model suggests that this relation is driven primarily by the high-luminosity end of the HMXB XLF. Our results have implications for binary population synthesis models, the nature of super-Eddington accreting objects (e.g., ultraluminous X-ray sources), recent efforts to identify active galactic nucleus candidates in dwarf galaxies, and the X-ray radiation fields in the early Universe during the epoch of cosmic heating at z > 10.},
   author = {Bret D. Lehmer and Rafael T. Eufrasio and Antara Basu-Zych and Keith Doore and Tassos Fragos and Kristen Garofali and Konstantinos Kovlakas and Benjamin J. Williams and Andreas Zezas and Luidhy Santana-Silva},
   month = {11},
   title = {The Metallicity Dependence of the High-Mass X-ray Binary Luminosity Function},
   url = {http://arxiv.org/abs/2011.09476},
   year = {2020},
}
@article{Wang2016,
   abstract = {Based on the recently completed \{\it Chandra\}/ACIS survey of X-ray point sources in nearby galaxies, we study the X-ray luminosity functions (XLFs) for X-ray point sources in different types of galaxies and the statistical properties of ultraluminous X-ray sources (ULXs). Uniform procedures are developed to compute the detection threshold, to estimate the foreground/background contamination, and to calculate the XLFs for individual galaxies and groups of galaxies, resulting in an XLF library for 343 galaxies of different types. With the large number of surveyed galaxies, we have studied the XLFs and ULX properties across different host galaxy types, and confirm with good statistics that the XLF slope flattens from lenticular ($\alpha\sim1.50\pm0.07$) to elliptical ($\sim1.21\pm0.02$), to spirals ($\sim0.80\pm0.02$), to peculiars ($\sim0.55\pm0.30$), and to irregulars ($\sim0.26\pm0.10$). The XLF break dividing the neutron star and black hole binaries is also confirmed, albeit at quite different break luminosities for different types of galaxies. A radial dependency is found for ellipticals, with a flatter XLF slope for sources located between $D_\{25\}$ and 2$D_\{25\}$, suggesting the XLF slopes in the outer region of early-type galaxies are dominated by low-mass X-ray binaries in globular clusters. This study shows that the ULX rate in early-type galaxies is $0.24\pm0.05$ ULXs per surveyed galaxy, on a $5\sigma$ confidence level. The XLF for ULXs in late-type galaxies extends smoothly until it drops abruptly around $4\times10^\{40\}$ erg s$^\{-1\}$, and this break may suggest a mild boundary between the stellar black hole population possibly including 30 $M_\odot$ black holes with super-Eddington radiation and intermediate mass black holes.},
   author = {Song Wang and Yanli Qiu and Jifeng Liu and Joel N. Bregman},
   doi = {10.3847/0004-637x/829/1/20},
   issn = {0004-637X},
   issue = {1},
   journal = {The Astrophysical Journal},
   month = {9},
   pages = {20},
   publisher = {American Astronomical Society},
   title = { CHANDRA ACIS SURVEY OF X-RAY POINT SOURCES IN NEARBY GALAXIES. II. X-RAY LUMINOSITY FUNCTIONS AND ULTRALUMINOUS X-RAY SOURCES },
   volume = {829},
   year = {2016},
}
@article{Mineo2013,
   abstract = {The colliding galaxy pair NGC 2207/IC 2163, at a distance of ∼39 Mpc, was observed with Chandra, and an analysis reveals 28 well resolved X-ray sources, including 21 ultraluminous X-ray sources (ULXs) with LX ≳ 1039 erg s-1, as well as the nucleus of NGC 2207. The number of ULXs is comparable with the largest numbers of ULXs per unit mass in any galaxy yet reported. In this paper we report on these sources, and quantify how their locations correlate with the local star formation rates seen in spatially resolved star formation rate density images that we have constructed using combinations of GALEX FUV and Spitzer 24 μm images. We show that the numbers of ULXs are strongly correlated with the local star formation rate densities surrounding the sources, but that the luminosities of these sources are not strongly correlated with star formation rate density. © 2013. The American Astronomical Society. All rights reserved..},
   author = {S. Mineo and S. Rappaport and B. Steinhorn and A. Levine and M. Gilfanov and D. Pooley},
   doi = {10.1088/0004-637X/771/2/133},
   issn = {15384357},
   issue = {2},
   journal = {Astrophysical Journal},
   keywords = {binaries: general,galaxies: individual (NGC 2207/IC 2163),galaxies: interactions,galaxies: nuclei,galaxies: starburst,galaxies: structure,stars: formation,stars: luminosity function, mass function,stars: neutron},
   month = {7},
   publisher = {Institute of Physics Publishing},
   title = {Spatially resolved star formation image and the ultraluminous x-ray source population in NGC 2207/IC 2163},
   volume = {771},
   year = {2013},
}
@article{appleton1997multiwavelength,
  title={Multiwavelength Observations of Collisional Ring Galaxies. I. Broad-Band Images, Global Properties, and Radial Colors of the Sample Galaxies},
  author={Appleton, PN and Marston, AP},
  journal={The Astronomical Journal},
  volume={113},
  pages={201--224},
  year={1997}
}

@article{blundell2007fluctuations,
  title={Fluctuations and symmetry in the speed and direction of the jets of SS 433 on different timescales},
  author={Blundell, Katherine M and Bowler, Michael G and Schmidtobreick, Linda},
  journal={Astronomy \& Astrophysics},
  volume={474},
  number={3},
  pages={903--910},
  year={2007},
  publisher={EDP Sciences}
}


@article{Middleton2017,
   abstract = {The ultraluminous X-ray source (ULX) population is known to contain neutron stars (NS), but the relative number of these compared to black hole (BH) primaries is unknown. Assuming classical supercritical accretion and resultant geometrical beaming, we show that the observed population ratio can be predicted from the mean masses of each family of compact objects and the relative spatial density of NSs to BHs. Conversely-and perhaps more importantly-given even a crude estimate for the spatial densities, an estimate of the fraction of the population containing NSs will begin to constrain the mean mass of BHs in ultraluminous X-ray sources.},
   author = {Matthew J. Middleton and Andrew King},
   doi = {10.1093/mnrasl/slx079},
   issn = {1745-3925},
   issue = {1},
   journal = {Monthly Notices of the Royal Astronomical Society: Letters},
   month = {9},
   pages = {L69-L71},
   publisher = {Oxford University Press (OUP)},
   title = {Predicting ultraluminous X-ray source demographics from geometrical beaming},
   volume = {470},
   year = {2017},
}

@INPROCEEDINGS{NSgtBH,
       author = {{Zi{\'o}{\l}kowski}, Janusz and {Belczy{\'n}ski}, Krzysztof},
        title = "{On the apparent lack of Be X-ray binaries with black holes in the galaxy and in the Magellanic Clouds}",
     keywords = {black holes: binaries, X-rays: binaries, (stars:) binaries: close, stars: evolution, stars: neutron, emission-line, Be, Astrophysics - Solar and Stellar Astrophysics},
    booktitle = {Jets at All Scales},
         year = 2011,
       editor = {{Romero}, Gustavo E. and {Sunyaev}, Rashid A. and {Belloni}, Tomaso},
       volume = {275},
        month = feb,
        pages = {329-330},
          doi = {10.1017/S1743921310016340},
archivePrefix = {arXiv},
       eprint = {1111.2330},
 primaryClass = {astro-ph.SR},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2011IAUS..275..329Z},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article{mineo2012x,
  title={X-ray emission from star-forming galaxies--I. High-mass X-ray binaries},
  author={Mineo, S and Gilfanov, M and Sunyaev, R},
  journal={Monthly Notices of the Royal Astronomical Society},
  volume={419},
  number={3},
  pages={2095--2115},
  year={2012},
  publisher={The Royal Astronomical Society}
}

@article{gao2003nonnuclear,
  title={Nonnuclear Hyper/Ultraluminous X-Ray Sources in the Starbursting Cartwheel Ring Galaxy},
  author={Gao, Yu and Wang, Q Daniel and Appleton, PN and Lucas, Ray A},
  journal={The Astrophysical Journal Letters},
  volume={596},
  number={2},
  pages={L171},
  year={2003},
  publisher={IOP Publishing}
}

@article{kuranov2007dynamical,
  title={On the dynamical formation of accreting intermediate mass black holes},
  author={Kuranov, AG and Popov, SB and Postnov, KA and Volonteri, M and Perna, R},
  journal={Monthly Notices of the Royal Astronomical Society},
  volume={377},
  number={2},
  pages={835--842},
  year={2007},
  publisher={Blackwell Publishing Ltd Oxford, UK}
}








